2024/04/17 by Chua, Gari Lincoln
#13A35 #13P99 #14B05 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.2404.10968
Given a prime number p and a positive integer m, we provide a family of diagonal hypersurfaces \ fn \n = 1∞ in m variables, for which the denominator of fpt (fn) (in lowest terms) is always p and whose F-pure thresholds stabilize after a certain n. We also provide another family of diagonal hypersurfaces \ gn \n = 1∞ in m variables, for which the power of p in the denominator of fpt (gn) (in lowest terms) diverges to ∞ as n → ∞. This behavior of the denominator of the F-pure thresholds is dependent on the congruence class of p modulo the smallest two exponents of \ fn \ and \ gn \.